TY - JOUR

T1 - The weak completion semantics and equality

AU - Saldanha, Emmanuelle Anna Dietz

AU - Hölldobler, Steffen

AU - Schwarz, Sibylle

AU - Stefanus, Lim Yohanes

N1 - Publisher Copyright:
© 2018, EasyChair. All rights reserved.

PY - 2018

Y1 - 2018

N2 - The weak completion semantics is an integrated and computational cognitive theory which is based on normal logic programs, three-valued ̷Lukasiewicz logic, weak completion, and skeptical abduction. It has been successfully applied – among others – to the suppression task, the selection task, and to human syllogistic reasoning. In order to solve ethical decision problems like – for example – trolley problems, we need to extend the weak completion semantics to deal with actions and causality. To this end we consider normal logic programs and a set E of equations as in the fluent calculus. We formally show that normal logic programs with equality admit a least E-model under the weak completion semantics and that this E-model can be computed as the least fixed point of an associated semantic operator. We show that the operator is not continuous in general, but is continuous if the logic program is a propositional, a finite-ground, or a finite datalog program and the Herbrand E-universe is finite. Finally, we show that the weak completion semantics with equality can solve a variety of ethical decision problems like the bystander case, the footbridge case, and the loop case by computing the least E-model and reasoning with respect to this E-model. The reasoning process involves counterfactuals which is necessary to model the different ethical dilemmas.

AB - The weak completion semantics is an integrated and computational cognitive theory which is based on normal logic programs, three-valued ̷Lukasiewicz logic, weak completion, and skeptical abduction. It has been successfully applied – among others – to the suppression task, the selection task, and to human syllogistic reasoning. In order to solve ethical decision problems like – for example – trolley problems, we need to extend the weak completion semantics to deal with actions and causality. To this end we consider normal logic programs and a set E of equations as in the fluent calculus. We formally show that normal logic programs with equality admit a least E-model under the weak completion semantics and that this E-model can be computed as the least fixed point of an associated semantic operator. We show that the operator is not continuous in general, but is continuous if the logic program is a propositional, a finite-ground, or a finite datalog program and the Herbrand E-universe is finite. Finally, we show that the weak completion semantics with equality can solve a variety of ethical decision problems like the bystander case, the footbridge case, and the loop case by computing the least E-model and reasoning with respect to this E-model. The reasoning process involves counterfactuals which is necessary to model the different ethical dilemmas.

UR - http://www.scopus.com/inward/record.url?scp=85068403198&partnerID=8YFLogxK

U2 - 10.29007/pr47

DO - 10.29007/pr47

M3 - Conference article

AN - SCOPUS:85068403198

VL - 57

SP - 326

EP - 342

JO - EPiC Series in Computing

JF - EPiC Series in Computing

SN - 2398-7340

T2 - 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, LPAR 2018

Y2 - 17 November 2018 through 21 November 2018

ER -